login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A085058
a(n) = A001511(n+1) + 1.
11
2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 7, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 8, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 7, 2, 3, 2, 4, 2, 3, 2, 5, 2
OFFSET
0,1
COMMENTS
Number of divisors of 2n+2 of the form 2^k. - Giovanni Teofilatto, Jul 25 2007
Number of steps for iteration of map x -> (3/2)*ceiling(x) to reach an integer when started at 2*n+1.
Also number of steps for iteration of map x -> (3/2)*floor(x) to reach an integer when started at 2*n+3. - Benoit Cloitre, Sep 27 2003
The first time that a(n) = e+1 is when n is of the form 2^e - 1. - Robert G. Wilson v, Sep 28 2003
Let 2^k(n) = largest power of 2 dividing tangent number A000182(n). Then a(n-1) = 2*n - k(n). - Yasutoshi Kohmoto, Dec 23 2006
a(n) is the number of integers generated by b(i+1) = (3+2n)*(b(i) + b(i-1))/2, following these two initial values, b(0) = b(1) = 1. Thereafter only non-integers are generated. - Richard R. Forberg, Nov 09 2014
a(n) is the 2-adic valuation of 4*n+4, which is equal to the number of trailing 1-bits of 4*n+3 in binary. - Ruud H.G. van Tol, Sep 11 2023
LINKS
J. C. Lagarias and N. J. A. Sloane, Approximate squaring, Experimental Math., 13 (2004), 113-128.
FORMULA
a(n) = A007814(3^(n+1) - (-1)^(n+1)) = A007814(A105723(n+1)). - Reinhard Zumkeller, Apr 18 2005
a(n) = A001511(n+1) + 1 = A001511(2*n+2). - Ray Chandler, Jul 29 2007
a(n) = A007814(5^(n+1) - 1). - Ivan Neretin, Jan 15 2016
a(n) = A007814(4*(n+1)) = A007814(n+1) + 2. - Ruud H.G. van Tol, Sep 11 2023
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3. - Amiram Eldar, Sep 13 2024
MAPLE
f := x->(3/2)*ceil(x); g := proc(n) local t1, c; global f; t1 := f(n); c := 1; while not type(t1, 'integer') do c := c+1; t1 := f(t1); od; RETURN([c, t1]); end;
a := n -> A001511(n+1) + 1: A001511 := n -> padic[ordp](2*n, 2): seq(a(n), n=0..104); # Johannes W. Meijer, Dec 22 2012
MATHEMATICA
g = 3 Ceiling[ # ]/2 &; f[n_?OddQ] := Length @ NestWhileList[ g, g[n], !IntegerQ[ # ] & ]; Table[ f[n], {n, 1, 210, 2}]
PROG
(PARI) A085058(n)=if(n<0, 0, c=2*n+7/2; x=0; while(frac(c)>0, c=3/2*floor(c); x++); x) \\ Benoit Cloitre, Sep 27 2003
(PARI) A085058(n)=if(n<0, 0, c=(2*n+1)*3/2; x=1; while(frac(c)>0, c=3/2*ceil(c); x++); x) \\ Benoit Cloitre, Sep 27 2003
(PARI) a(n) = valuation(n+1, 2)+2; \\ Michel Marcus, Jan 15 2016
(Magma) [Valuation(n+1, 2)+2: n in [0..100]]; // Vincenzo Librandi, Jan 16 2016
(Python)
def A085058(n): return (~(n+1) & n).bit_length()+2 # Chai Wah Wu, Apr 14 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 11 2003
EXTENSIONS
Edited by Franklin T. Adams-Watters, Dec 09 2013
STATUS
approved